1. am * an = a(m+n) says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it’s the same as taking that number a and raising it to a power equal to the sum of m + n.
Here’s an example where
a = 3
m = 4
n = 5
am * an = a(m+n)
34 * 35 = 3(4+5) = 39 = 19,683
2. (a * b)n = an * bn says that when you multiply two numbers, and then multiply that product by itself n times, it’s the same as multiplying the first number by itself n times and multiplying that by the second number multiplied by itself n times.
Let’s work out an example where
a = 3
b = 6
n = 5
(a * b)n = an * bn
(3 * 6)5 = 35 * 65
185 = 35 * 65 = 243 * 7,776 = 1,889,568
3. (am)n = a(m * n) says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it’s the same as multiplying the number a by itself m * n times.
Let’s work out an example where
a = 3
m = 4
n = 5
(am)n = a(m * n)
(34)5 = 3(4 * 5) = 320 = 3,486,784,401
4. am / an = a(m-n) says that when you take a number, a, and multiply it by itself m times, then divide that product by a multiplied by itself n times, it’s the same as a multiplied by itself m-n times.
Here’s an example where
a = 3
m = 4
n = 5
am / an = a(m-n)
34 / 35 = 3(4-5) = 3-1 (Remember how to raise a number to a negative exponent.)
Step-by-step explanation:
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There are five rules for working with exponents:
1. am * an = a(m+n)
2. (a * b)n = an * bn
3. (am)n = a(m * n)
4. am / an = a(m-n)
5. (a/b)n = an / bn
Let’s look at each of these in detail.
1. am * an = a(m+n) says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it’s the same as taking that number a and raising it to a power equal to the sum of m + n.
Here’s an example where
a = 3
m = 4
n = 5
am * an = a(m+n)
34 * 35 = 3(4+5) = 39 = 19,683
2. (a * b)n = an * bn says that when you multiply two numbers, and then multiply that product by itself n times, it’s the same as multiplying the first number by itself n times and multiplying that by the second number multiplied by itself n times.
Let’s work out an example where
a = 3
b = 6
n = 5
(a * b)n = an * bn
(3 * 6)5 = 35 * 65
185 = 35 * 65 = 243 * 7,776 = 1,889,568
3. (am)n = a(m * n) says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it’s the same as multiplying the number a by itself m * n times.
Let’s work out an example where
a = 3
m = 4
n = 5
(am)n = a(m * n)
(34)5 = 3(4 * 5) = 320 = 3,486,784,401
4. am / an = a(m-n) says that when you take a number, a, and multiply it by itself m times, then divide that product by a multiplied by itself n times, it’s the same as a multiplied by itself m-n times.
Here’s an example where
a = 3
m = 4
n = 5
am / an = a(m-n)
34 / 35 = 3(4-5) = 3-1 (Remember how to raise a number to a negative exponent.)
34 / 35 = 1 / 31 = 1/3